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2 years ago

THIS IS DUE SOON! PLEASE SOMEONE HELP!!! IM SO CONFUSED!!! SHOW ME STEP BY STEP PLEASE! QUESTION IS IN PICTURE BELOW!

Mathematics

1 answer:

Citrus2011 [14]2 years ago

4 0

Answer:

62.2°

Step-by-step explanation:

formula to count area of triangle

1) √[(s)(s-a)(s-b)(s-c)] , s= (a+b+c)/2

2) 1/2ab sin c

count the area first

s=(8+5+9)/2

=11

area=√[(11)(11-8)(11-5)(11-9)]

= √396

=19.8997

1/2(5)(9) sin c = 19.8997

sin c = 19.8997(2)/45

sin c = 0.8844

c = sin-¹ 0.8844

c = 62.2° (nearest tenth)

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Which of the following definite integrals could be used to calculate the total area bounded by the graph of y = x^3 – 3x^2 + 2x

castortr0y [4]

Answer: The correct option is second, i.e. ,"2 times the integral from 0 to 1 of the quantity x cubed minus 3 times x squared plus 2 times x, dx".

Explanation:

The given equation is,

$y=x^3-3x^2+2x$

It can be written as,

$f(x)=x^3-3x^2+2x$

Find the zeros of the equation. Equation the function equal to 0.

$0=x^3-3x^2+2x$

$x(x^2-3x+2)=0$

$x(x^2-2x-x+2)=0$

$x(x-2)(x-1)=0$

So, the three zeros are 0, 1 and 2.

The graph of the equation is shown below.

From the given graph it is noticed that the enclosed by the curve and x- axis is lies between 0 to 2, but the area from 0 to 1 lies above the x-axis and area from 1 to 2 lies below the x-axis. So the function will be negative from 1 to 2.

The area enclosed by curve and x-axis is,

$A=\int_{0}^{1}f(x)dx+\int_{1}^{2}[-f(x)]dx$

$A=\int_{0}^{1}f(x)dx-\int_{1}^{2}f(x)dx$

From the graph it is noticed that the area from 0 to 1 is symmetric or same as area from 1 to 2. So the total area is the twice of area from 0 to 1.

$A=2\int_{0}^{1}f(x)dx$

$A=2\int_{0}^{1}[x^3-3x^2+2x]dx$

Therefore, The correct option is "2 times the integral from 0 to 1 of the quantity x cubed minus 3 times x squared plus 2 times x, dx".

3 0

3 years ago

What is 1/3 x 12 help me quick

MArishka [77]

Answer:

12/3 = 4

Step-by-step explanation:

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3 years ago

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Bob has $1.15 in his wallet which contains 18 coins in nickels and dimes. Find how many nickles he has.

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Answer:

13 nickels

Step-by-step explanation:

Let n represent the number of nickels Bob has. Then 18-n is the number of dimes, and the total value (in cents) is ...

5n +10(18-n) = 115

-5n +180 = 115 . . . simplify

65 = 5n . . . . . add 5n-115

13 = n . . . . . . . divide by 5

Bob has 13 nickels.

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3 years ago

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